What does ‘balance preamp’ mean?

An additional advantage of balanced preamps is that they have improved immunity to noise in the power supplies of the preamp. This is because any such noise is common to both phases of the signal and so it less able to be amplified as opposed to a single-ended circuit.

No, a real balanced circuit is one where the positive (+), the negative (-) have distinct circuits, and negative is distinct from earth.So there is a higher manufacturing cost. There is also noise cancellation -- i.e. any noise common in both circuits is cancelled out -- hence, balanced is used in professional audio applications which are noisy environments.

^^ This. Its not hype- just better technology.